function rdp_find_max(points, start, end) {
    const EPS = 0.5;

    let result = -1;
    let max_dist = 0;

    const a = points[start];
    const b = points[end];

    const dx = b.x - a.x;
    const dy = b.y - a.y;

    const dist_ab = Math.sqrt(dx * dx + dy * dy);
    const sin_theta = dy / dist_ab;
    const cos_theta = dx / dist_ab;

    for (let i = start; i < end; ++i) {
        const p = points[i];
        
        const ox = p.x - a.x;
        const oy = p.y - a.y;

        const rx = cos_theta * ox + sin_theta * oy;
        const ry = -sin_theta * ox + cos_theta * oy;

        const x = rx + a.x;
        const y = ry + a.y;

        const dist = Math.abs(y - a.y);

        if (dist > EPS && dist > max_dist) {
            result = i;
            max_dist = dist;
        }
    }

    return result;
}

function process_rdp_r(points, start, end) {
    let result = [];
    
    const max = rdp_find_max(points, start, end);

    if (max !== -1) {
        const before = process_rdp_r(points, start, max);
        const after = process_rdp_r(points, max, end);
        result = [...before, points[max], ...after];
    }

    return result;
}

function process_rdp(points) {
    const result = process_rdp_r(points, 0, points.length - 1);
    result.unshift(points[0]);
    result.push(points[points.length - 1]);
    return result;
}

function process_ewmv(points, round = false) {
    const result = [];
    const alpha = 0.4;

    result.push(points[0]);

    for (let i = 1; i < points.length; ++i) {
        const p = points[i];
        const x = Math.round(alpha * p.x + (1 - alpha) * result[result.length - 1].x);
        const y = Math.round(alpha * p.y + (1 - alpha) * result[result.length - 1].y);
        result.push({'x': x, 'y': y});
    }

    return result;
}

function process_stroke(points) {
    const result0 = process_ewmv(points);
    const result1 = process_rdp(result0, true);
    return result1;
}

function stroke_stats(points, width) {
    let length = 0;
    let xmin = points[0].x, ymin = points[0].y;
    let xmax = xmin, ymax = ymin;

    for (let i = 0; i < points.length; ++i) {
        const point = points[i];
        if (point.x < xmin) xmin = point.x;
        if (point.y < ymin) ymin = point.y;
        if (point.x > xmax) xmax = point.x;
        if (point.y > ymax) ymax = point.y;

        if (i > 0) {
            const last = points[i - 1];
            const dx = point.x - last.x;
            const dy = point.y - last.y;
            length += Math.sqrt(dx * dx + dy * dy);
        }
    }

    xmin -= width;
    ymin -= width;
    xmax += width * 2;
    ymax += width * 2;

    const bbox = {
        'xmin': Math.floor(xmin),
        'ymin': Math.floor(ymin),
        'xmax': Math.ceil(xmax),
        'ymax': Math.ceil(ymax)
    };

    return {
        'bbox': bbox,
        'length': length,
    };
}

function rectangles_intersect(a, b) {
    const result = (
        a.xmin <= b.xmax
        && a.xmax >= b.xmin
        && a.ymin <= b.ymax 
        && a.ymax >= b.ymin
    );

    return result;
}

function stroke_intersects_region(points, bbox) {
    const stats = stroke_stats(points, storage.cursor.width);
    return rectangles_intersect(stats.bbox, bbox);
}